Sample Definition

Our research will focus on the scale of census tracts in Massachusetts, with a look at adult characteristics and behaviors aggregated to the level of census tracts.

Load data

library(tidyverse)

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## ✓ readr   2.0.1     ✓ forcats 0.5.1

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library(tidycensus)
library(readxl)
library(knitr)
library(sf)

## Linking to GEOS 3.8.1, GDAL 3.2.1, PROJ 7.2.1

library(gridExtra)

## 
## Attaching package: 'gridExtra'

## The following object is masked from 'package:dplyr':
## 
##     combine

library(ggthemes)
library(ggspatial)
library(jtools)
library(tigris)

## To enable 
## caching of data, set `options(tigris_use_cache = TRUE)` in your R script or .Rprofile.

library(huxtable)

## 
## Attaching package: 'huxtable'

## The following object is masked from 'package:dplyr':
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## The following object is masked from 'package:ggplot2':
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Mode of Transportation

Source: American Community Survey (2019)

• Mode of Transportation

acs_transport <- get_acs(geography = "tract", 
                        year = 2019,
                        variables = c(transport_any = "B08301_001E",
                                      transport_walk = "B08301_019E",
                                      transport_car = "B08301_002E",
                                      transport_public = "B08301_010E",
                                      transport_bike = "B08301_018E",
                                      transport_taxi = "B08301_016E",
                                      transport_motorcycle = "B08301_017E",
                                      transport_other = "B08301_020E"),
                        state = "MA",
                        output = "wide",
                        geometry = FALSE) %>%
  mutate(pct_walk = transport_walk / transport_any) %>%
  mutate(pct_car = transport_car / transport_any) %>%
  mutate(pct_public = transport_public / transport_any) %>%
  mutate(pct_bike = transport_bike / transport_any) %>%
  mutate(pct_taxi = transport_taxi / transport_any) %>%
  mutate(pct_motorcycle = transport_motorcycle / transport_any) %>%
  mutate(pct_other = transport_other / transport_any)%>%
  select(GEOID, pct_walk, pct_car, pct_public, pct_bike, pct_taxi, pct_motorcycle, pct_other)

Demographics

Source: American Community Survey (2019)

• Majority White vs. Non-White (categorical)
• Majority Female vs. Not Female (categorical)

race_majority <- get_acs(geography = "tract", 
                        year = 2019,
                        variables = c( total_pop = "B02001_001",
                                       white_pop = "B02001_002"),
                        state = "MA",
                        output = "wide",
                        geometry = FALSE) %>%
  mutate(white_majority = case_when(white_popE / total_popE >= .5 ~ "Majority White",
                          white_popE / total_popE < .5 ~ "Non-Majority White",
                          TRUE ~ "unknown")) %>%
  select(GEOID,white_majority)

## Getting data from the 2015-2019 5-year ACS

sex_majority <- get_acs(geography = "tract", 
                        year = 2019,
                        variables = c( total_pop = "B01001_001",
                                       female_pop = "B01001_026"),
                        state = "MA",
                        output = "wide",
                        geometry = FALSE) %>%
  mutate(female_majority = case_when(female_popE / total_popE >= .5 ~ "Female Majority",
                          female_popE / total_popE < .5 ~ "Non-Female Majority",
                          TRUE ~ "unknown")) %>%
  select(GEOID,female_majority)

## Getting data from the 2015-2019 5-year ACS

U.S. Chronic Disease Indicators

Source: United States Centers for Disease Control and Prevention: PLACES U.S. Chronic Disease Indicators

• Population Percentage with Current Mental Health Issues (continuous)
• Population Percentage with Obesity (continuous)
• Population Percentage with Current Asthma (continuous)

Mental_Health <- read_csv('data/PLACES__Local_Data_for_Better_Health__Census_Tract_Data_2020_release.csv') %>%
  filter(Year == 2018) %>%
  filter(Short_Question_Text == "Mental Health") %>%
  filter(StateAbbr == "MA") %>%
  rename(GEOID = LocationID) %>%
  group_by(GEOID) %>%
  rename(pct_mental = Data_Value) %>%
  select(GEOID, pct_mental, Data_Value_Unit)

## Warning: One or more parsing issues, see `problems()` for details

## Rows: 2024865 Columns: 23

## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (16): StateAbbr, StateDesc, CountyName, CountyFIPS, LocationName, DataSo...
## dbl  (5): Year, Data_Value, Low_Confidence_Limit, High_Confidence_Limit, Tot...
## lgl  (2): Data_Value_Footnote_Symbol, Data_Value_Footnote

## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
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Asthma <- read_csv('data/PLACES__Local_Data_for_Better_Health__Census_Tract_Data_2020_release.csv') %>%
  filter(Year == 2018) %>%
  filter(Short_Question_Text == "Current Asthma") %>%
  filter(StateAbbr == "MA") %>%
  rename(GEOID = LocationID) %>%
  group_by(GEOID) %>%
  rename(pct_asthma = Data_Value) %>%
  select(GEOID, pct_asthma, Data_Value_Unit)

## Warning: One or more parsing issues, see `problems()` for details

## Rows: 2024865 Columns: 23

## ── Column specification ────────────────────────────────────────────────────────
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## chr (16): StateAbbr, StateDesc, CountyName, CountyFIPS, LocationName, DataSo...
## dbl  (5): Year, Data_Value, Low_Confidence_Limit, High_Confidence_Limit, Tot...
## lgl  (2): Data_Value_Footnote_Symbol, Data_Value_Footnote

## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Obesity <- read_csv('data/PLACES__Local_Data_for_Better_Health__Census_Tract_Data_2020_release.csv') %>%
  filter(Year == 2018) %>%
  filter(Short_Question_Text == "Obesity") %>%
  filter(StateAbbr == "MA") %>%
  rename(GEOID = LocationID) %>%
  group_by(GEOID) %>%
  rename(pct_obesity = Data_Value) %>%
  select(GEOID, pct_obesity, Data_Value_Unit)

## Warning: One or more parsing issues, see `problems()` for details

## Rows: 2024865 Columns: 23

## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (16): StateAbbr, StateDesc, CountyName, CountyFIPS, LocationName, DataSo...
## dbl  (5): Year, Data_Value, Low_Confidence_Limit, High_Confidence_Limit, Tot...
## lgl  (2): Data_Value_Footnote_Symbol, Data_Value_Footnote

## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Walkability

Source: United States Environmental Protection Agency: National Walkability Index

• Walkability Index Score

# The following code was used to created the original "Walkability" file, it was then re-loaded as a .shp file
# This was done to reduce the file size and because the .shp file doesn't except "avg_w_ind" as a column name (too long apparently).

# Walkability <- st_read(dsn = "Natl_WI.gdb") %>%
#   filter(STATEFP == "25") %>%
#   select(GEOID10, NatWalkInd, TotPop) %>%
#   mutate(tract = substr(GEOID10, 1, 11)) %>%
#   st_set_geometry(NULL) %>%
#   group_by(tract) %>%
#   summarise(avg_w_ind = weighted.mean(NatWalkInd, TotPop)) %>%
#   rename(GEOID = tract)
# 
# st_write(Walkability, "data/Walkability_file.shp")
# print(Walkability)

Walkability <- st_read(dsn = "data/Walkability_file.dbf")

## Reading layer `Walkability_file' from data source 
##   `/Users/mc/Documents/2_ SCHOOL/2_ Harvard/1_ Classes/S1/6_ Quant/Assignment 5/quant_assignment_1/data/Walkability_file.dbf' 
##   using driver `ESRI Shapefile'

## Warning: no simple feature geometries present: returning a data.frame or tbl_df

Walkability and Health Metrics

Walkability and Asthma

cor.test(~ avg_w_ind + pct_asthma, data = data)

## 
##  Pearson's product-moment correlation
## 
## data:  avg_w_ind and pct_asthma
## t = 11.883, df = 1461, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2494104 0.3428982
## sample estimates:
##       cor 
## 0.2968655

age_model <- lm(avg_w_ind ~ pct_asthma, data = data)

summary(age_model)

## 
## Call:
## lm(formula = avg_w_ind ~ pct_asthma, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.8997  -3.1243   0.3704   2.9462   8.7244 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   2.4426     0.7741   3.155  0.00164 ** 
## pct_asthma    0.8722     0.0734  11.883  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.723 on 1461 degrees of freedom
##   (15 observations deleted due to missingness)
## Multiple R-squared:  0.08813,    Adjusted R-squared:  0.0875 
## F-statistic: 141.2 on 1 and 1461 DF,  p-value: < 2.2e-16

ggplot(data) +
  geom_point(aes(x = avg_w_ind, y = pct_asthma)) +
  geom_smooth(aes(x = avg_w_ind, y = pct_asthma), color = 'red', method = 'lm', se = FALSE) +
  labs(x = "Walkability Score", 
       y = "Percent of Pop. with Asthma", 
       title = "Regression: Walkability Score and Asthma Rates, Correlation: 0.29")

For asthma, the 95-percent confidence interval for the correlation does not include zero - all values in the interval are positive. Additionally, this finding is supported by the regression, with an R-squared value of 0.08 and a p-value of less than 0.05. This means we can say with 95-percent confidence that higher asthma rates are associated with more walkable census tracts and that it is statistically significant.

Walkability and Obesity

cor.test(~ avg_w_ind + pct_obesity, data = data)

## 
##  Pearson's product-moment correlation
## 
## data:  avg_w_ind and pct_obesity
## t = -0.48809, df = 1461, p-value = 0.6256
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.06397625  0.03850640
## sample estimates:
##         cor 
## -0.01276846

age_model <- lm(avg_w_ind ~ pct_obesity, data = data)

summary(age_model)

## 
## Call:
## lm(formula = avg_w_ind ~ pct_obesity, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.8134 -3.5706  0.9706  3.2836  7.4787 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 11.798894   0.484225  24.367   <2e-16 ***
## pct_obesity -0.008676   0.017775  -0.488    0.626    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.899 on 1461 degrees of freedom
##   (15 observations deleted due to missingness)
## Multiple R-squared:  0.000163,   Adjusted R-squared:  -0.0005213 
## F-statistic: 0.2382 on 1 and 1461 DF,  p-value: 0.6256

ggplot(data) +
  geom_point(aes(x = avg_w_ind, y = pct_obesity)) +
  geom_smooth(aes(x = avg_w_ind, y = pct_obesity), color = 'red', method = 'lm', se = FALSE) +
  labs(x = "Walkability Score", 
       y = "Percent of Pop. with Obesity", 
       title = "Regression: Walkability Score and Obesity Rates, Correlation: -0.01")

For obesity, the 95-percent confidence interval for the correlation includes zero, meaning the direction of the correlation (positive or negative) is uncertain. Additionally, this finding is supported by the regression, with an R-squared value of -0.00052 and a p-value of 0.625. This means we cannot inform with with confidence whether obesity and walkable census tracts are correlated and that this finding’s significance is indeterminable with the present evidence.

Walkability and Mental Health

cor.test(~ avg_w_ind + pct_mental, data = data)

## 
##  Pearson's product-moment correlation
## 
## data:  avg_w_ind and pct_mental
## t = 13.737, df = 1461, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2920163 0.3828188
## sample estimates:
##       cor 
## 0.3382045

age_model <- lm(avg_w_ind ~ pct_mental, data = data)

summary(age_model)

## 
## Call:
## lm(formula = avg_w_ind ~ pct_mental, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.7242  -2.9927   0.3731   2.9256   8.3049 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.08786    0.41030   14.84   <2e-16 ***
## pct_mental   0.39927    0.02907   13.74   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.669 on 1461 degrees of freedom
##   (15 observations deleted due to missingness)
## Multiple R-squared:  0.1144, Adjusted R-squared:  0.1138 
## F-statistic: 188.7 on 1 and 1461 DF,  p-value: < 2.2e-16

ggplot(data) +
  geom_point(aes(x = avg_w_ind, y = pct_mental)) +
  geom_smooth(aes(x = avg_w_ind, y = pct_mental), color = 'red', method = 'lm', se = FALSE) +
  labs(x = "Walkability Score", 
       y = "Percent of Pop. with Mental Health Issues", 
       title = "Regression: Walkability Score and Mental Health Rates, Correlation: 0.33")

For mental health, the 95-percent confidence interval for the correlation does not include zero - all values in the interval are positive. Additionally, this finding is supported by the regression, with an R-squared value of 0.11 and a p-value of less than 0.05. This means we can say with 95-percent confidence that higher incidence of mental health issues are associated with more walkable census tracts and that this finding is statistically significant.

Walkability and Commute Choice

Walkability and Commuting by Walking

cor.test(~ avg_w_ind + pct_walk, data = data)

## 
##  Pearson's product-moment correlation
## 
## data:  avg_w_ind and pct_walk
## t = 16.317, df = 1462, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3482749 0.4349887
## sample estimates:
##       cor 
## 0.3925036

age_model <- lm(avg_w_ind ~ pct_walk, data = data)

summary(age_model)

## 
## Call:
## lm(formula = avg_w_ind ~ pct_walk, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.8213  -3.1892   0.6462   3.0897   7.3097 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  10.7073     0.1075   99.60   <2e-16 ***
## pct_walk     15.2938     0.9373   16.32   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.594 on 1462 degrees of freedom
##   (14 observations deleted due to missingness)
## Multiple R-squared:  0.1541, Adjusted R-squared:  0.1535 
## F-statistic: 266.3 on 1 and 1462 DF,  p-value: < 2.2e-16

ggplot(data) +
  geom_point(aes(x = avg_w_ind, y = pct_walk)) +
  geom_smooth(aes(x = avg_w_ind, y = pct_walk), color = 'red', method = 'lm', se = FALSE) +
  labs(x = "Walkability Score", 
       y = "Percent of Pop. Commuting Via Walking", 
       title = "Regression: Walkability Score and Walking Use, Correlation: 0.39")

For commuting by walking, the 95-percent confidence interval for the correlation does not include zero - all values in the interval are positive. Additionally, this finding is supported by the regression, with an R-squared value of 0.15 and a p-value of less than 0.05. This means we can say with 95-percent confidence that higher commuting rates by walking are associated with more walkable census tracts and that this finding is statistically significant.

Walkability and Commuting by Biking

cor.test(~ avg_w_ind + pct_bike, data = data)

## 
##  Pearson's product-moment correlation
## 
## data:  avg_w_ind and pct_bike
## t = 14.107, df = 1462, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3002402 0.3904558
## sample estimates:
##      cor 
## 0.346148

age_model <- lm(avg_w_ind ~ pct_bike, data = data)

summary(age_model)

## 
## Call:
## lm(formula = avg_w_ind ~ pct_bike, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -9.9704 -3.2022  0.5954  3.0827  7.7655 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  10.9704     0.1045  104.94   <2e-16 ***
## pct_bike     66.4250     4.7085   14.11   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.666 on 1462 degrees of freedom
##   (14 observations deleted due to missingness)
## Multiple R-squared:  0.1198, Adjusted R-squared:  0.1192 
## F-statistic:   199 on 1 and 1462 DF,  p-value: < 2.2e-16

ggplot(data) +
  geom_point(aes(x = avg_w_ind, y = pct_bike)) +
  geom_smooth(aes(x = avg_w_ind, y = pct_bike), color = 'blue', method = 'lm', se = FALSE) +
  labs(x = "Walkability Score", 
       y = "Percent of Pop. Commuting Via Biking", 
       title = "Regression: Walkability Score and Biking Use, Correlation: 0.34")

For commuting by biking, the 95-percent confidence interval for the correlation does not include zero - all values in the interval are positive. Additionally, this finding is supported by the regression, with an R-squared value of 0.11 and a p-value of less than 0.05. This means we can say with 95-percent confidence that higher commuting rates by biking are associated with more walkable census tracts and that this finding is statistically significant.

Walkability and Commuting by Public Transit

cor.test(~ avg_w_ind + pct_public, data = data)

## 
##  Pearson's product-moment correlation
## 
## data:  avg_w_ind and pct_public
## t = 19.814, df = 1462, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.4187422 0.4995602
## sample estimates:
##       cor 
## 0.4601037

age_model <- lm(avg_w_ind ~ pct_public, data = data)

summary(age_model)

## 
## Call:
## lm(formula = avg_w_ind ~ pct_public, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -22.7747  -2.8021   0.2858   2.7100   8.1044 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  10.1272     0.1160   87.31   <2e-16 ***
## pct_public   13.6476     0.6888   19.81   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.469 on 1462 degrees of freedom
##   (14 observations deleted due to missingness)
## Multiple R-squared:  0.2117, Adjusted R-squared:  0.2112 
## F-statistic: 392.6 on 1 and 1462 DF,  p-value: < 2.2e-16

ggplot(data) +
  geom_point(aes(x = avg_w_ind, y = pct_public)) +
  geom_smooth(aes(x = avg_w_ind, y = pct_public), color = 'green', method = 'lm', se = FALSE) +
  labs(x = "Walkability Score", 
       y = "Percent of Pop. Commuting Via Transit", 
       title = "Regression: Walkability Score and Transit Use, Correlation: 0.46")

For commuting by transit, the 95-percent confidence interval for the correlation does not include zero - all values in the interval are positive. Additionally, this finding is supported by the regression, with an R-squared value of 0.21 and a p-value of less than 0.05. This means we can say with 95-percent confidence that higher commuting rates by transit are associated with more walkable census tracts and that this finding is statistically significant.

Walkability and Commuting by Car

cor.test(~ avg_w_ind + pct_car, data = data)

## 
##  Pearson's product-moment correlation
## 
## data:  avg_w_ind and pct_car
## t = -23.1, df = 1462, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.5536691 -0.4785508
## sample estimates:
##       cor 
## -0.517105

age_model <- lm(avg_w_ind ~ pct_car, data = data)

summary(age_model)

## 
## Call:
## lm(formula = avg_w_ind ~ pct_car, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -18.2611  -2.7227   0.1955   2.6107   8.0268 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  19.2611     0.3446   55.89   <2e-16 ***
## pct_car     -10.0765     0.4362  -23.10   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.344 on 1462 degrees of freedom
##   (14 observations deleted due to missingness)
## Multiple R-squared:  0.2674, Adjusted R-squared:  0.2669 
## F-statistic: 533.6 on 1 and 1462 DF,  p-value: < 2.2e-16

ggplot(data) +
  geom_point(aes(x = avg_w_ind, y = pct_car)) +
  geom_smooth(aes(x = avg_w_ind, y = pct_car), color = 'orange', method = 'lm', se = FALSE) +
  labs(x = "Walkability Score", 
       y = "Percent of Pop. Commuting Via Car", 
       title = "Regression: Walkability Score and Car Use, Correlation: -0.51")

For commuting by car, the 95-percent confidence interval for the correlation does not include zero - all values in the interval are negative. Additionally, this finding is supported by the regression, with an R-squared value of 0.26 and a p-value of less than 0.05. This means we can say with 95-percent confidence that lower commuting rates by car are associated with more walkable census tracts and that this finding is statistically significant.

Categorical variables

sex_model <- lm(avg_w_ind ~ female_majority, data = data)

summary(sex_model)

## 
## Call:
## lm(formula = avg_w_ind ~ female_majority, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -10.402  -3.602   0.950   3.292   7.702 
## 
## Coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                         11.6292     0.1222   95.13   <2e-16 ***
## female_majorityNon-Female Majority  -0.2267     0.2222   -1.02    0.308    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.906 on 1462 degrees of freedom
##   (14 observations deleted due to missingness)
## Multiple R-squared:  0.0007113,  Adjusted R-squared:  2.781e-05 
## F-statistic: 1.041 on 1 and 1462 DF,  p-value: 0.3078

ggplot(data) +
  geom_point(aes(x = avg_w_ind, y = female_majority)) +
  geom_smooth(aes(x = avg_w_ind, y = female_majority), color = 'orange', method = 'lm', se = FALSE) +
  labs(x = "Walkability Score", 
       y = "Percent of Pop. that identify as female", 
       title = "Walkability Score by Sex")

race_model <- lm(avg_w_ind ~ white_majority, data = data)

summary(race_model)

## 
## Call:
## lm(formula = avg_w_ind ~ white_majority, data = data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.9151  -3.2729   0.3703   3.1949   7.8655 
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                       11.2386     0.1039 108.125   <2e-16 ***
## white_majorityNon-Majority White   3.3431     0.3349   9.981   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.781 on 1462 degrees of freedom
##   (14 observations deleted due to missingness)
## Multiple R-squared:  0.0638, Adjusted R-squared:  0.06316 
## F-statistic: 99.63 on 1 and 1462 DF,  p-value: < 2.2e-16

ggplot(data) +
  geom_point(aes(x = avg_w_ind, y = white_majority)) +
  geom_smooth(aes(x = avg_w_ind, y = white_majority), color = 'orange', method = 'lm', se = FALSE) +
  labs(x = "Walkability Score", 
       y = "Percent of Pop. that identify as White", 
       title = "Walkability Score by Race")

Analysis

In our multi-variate regression, we noticed that our intercept was a negative number. We found this interesting for interpretation because the regression table as originally estimated tells us that if all other variables (means of commute, certain health indicators, and ) are held at zero, we would expect a negative Walkability Index Score. Given it’s not possible to have a negative Walkability Index score, we thought it would be valuable to mean center our continuous variables in order to see how the intercept value might shift if all variables were end at their mean value.

What we found in the process of mean centering our data did very little to improve the overall analysis of our regression table. With a p-value of .96, the mean-centered intercept was statistically insignificant. Even if it had produced a significant p-value, the estimated walkability score of 0 does not offer any new insight as once again this isn’t a possible score on the Walkability Index (1-20). As expected, all other estimated coefficient values stayed constant despite the mean-centering. Ultimately, we prefer this second model, as it shows that mean-centering has been attempted (as opposed to not addressing the negative intercept value in the non-mean centered multi-variate regression) but we acknowledge this does not offer any new insight.